Bitcoins are all the rage these days. They are a virtual currency, with their value determined by cryptographic computer effort, but can be used to buy real things.
One way of generating bitcoins is by embedding a widget on a webpage, and that is what I've done on this page! The miner should now be running in the background (if you allowed the Java applet to do so), and it is automatically generating bitcoin for me. If you want to stop it, click the 'Stop' link below.
Storing bitcoins: I'm using the original Bitcoin wallet, available at bitcoin.org.
An explanation of Bitcoin: Bitcoin: A Peer-to-Peer Electronic Cash System (PDF) by Satoshi Nakamoto is a nine-page summary of the Bitcoin architecture and its algorithms.